consecutive square numbers
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Multiply each preceding term by 4.
The rule is 5, 10, 15 and so the next number will be 20+31 = 51
Everytime you move to the next number you add 1, then 2, then 3, etc.1+1=22+2=44+3=77+4=1111+5=1616+6=2222+7=2929+8=37
There are actually more than a pattern rule for that type of sequence. The pattern rule is not obvious. The sequence is actually this: an = 5a(n - 2) for n > 2, such that the seed values are a1 = 1 and a2 = 5. Another pattern rule is the number of palindromes using a maximum of five different symbols. The third one is the Inverse Binomial Mean transformation of the Fibonacci sequence.
So you're adding 3, 5, 7, 9, 11 etc 1, 4, 9, 16, 25, 36, 49